Growth and uniqueness of rank

Eli Aljadeff*, Shmuel Rosset

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We prove that algebras of sub-exponential growth and, more generally, rings with a sub-exponential "growth structure" have the unique rank property. In the opposite direction the proof shows that if the rank is not unique one gets lower bounds on the exponent of growth. Fixing the growth exponent it shows that an isomorphism between free modules of greatly differing ranks can only be implemented by matrices with entries of logarithmically proportional high degrees.

Original languageEnglish
Pages (from-to)251-256
Number of pages6
JournalIsrael Journal of Mathematics
Volume64
Issue number2
DOIs
StatePublished - Jun 1988
Externally publishedYes

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